Related papers: The augmented Block Cimmino algorithm revisited
The incremental least mean square (ILMS) algorithm was presented in \cite{Lopes2007}. The article included theoretical analysis of the algorithm along with simulation results under different scenarios. However, the transient analysis was…
We present an Alternating Direction Method of Multipliers (ADMM) algorithm for solving optimization problems with an l_1 regularized least-squares cost function subject to recursive equality constraints. The considered optimization problem…
Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which being the solver for the least squares problem $\min_{x}\lVert b-Ax\rVert_{2}$. By transforming least…
This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…
Because of the relevance of the results, this paper is merged into the paper titled "On the Number of Solutions to Asymptotic Plateau Problem" (arXiv:math.DG/0505593) as a new section.
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
Least-squares optimized polynomials are discussed which are needed in the two-step multi-bosonic algorithm for Monte Carlo simulations of quantum field theories with fermions. A recurrence scheme for the calculation of necessary…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
The threshold estimate derived in previous versions of this paper was incorrect; this note explains the flaw. A new proof is discussed in arXiv:0809.5063.
There is a continuing effort to support and prepare the precision physics programs for the present and planned future colliders such as HL-LHC, FCC, CLIC, CEPC, and CPPC. We discuss new results from IR-improved amplitude-based resummation…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
In this chapter we present the sums of Hermitian squares approach to noncommutative polynomial optimization problems. This is an extension of the sums of squares approach for polynomial optimization arising from real algebraic geometry. We…
Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special…
Naturally complex-valued information or those presented in complex domain are effectively processed by an augmented complex least-mean-square (ACLMS) algorithm. In some applications, the ACLMS algorithm may be too computationally- and…
We consider estimating an unknown signal, both blocky and sparse, which is corrupted by additive noise. We study three interrelated least squares procedures and their asymptotic properties. The first procedure is the fused lasso, put…
In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present explicit and self-contained proof for all of them,…
We study matrix inequalities involving partial traces for positive semidefinite block matrices. First of all, we present a new method to prove a celebrated result of Choi [Linear Algebra Appl. 516 (2017)]. Our method also allows us to prove…
In the paper, some lower bounds for polygamma functions are refined.
In this paper, we consider nonconvex optimization problems with nonsmooth nonconvex objective function and nonlinear equality constraints. We assume that both the objective function and the functional constraints can be separated into 2…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.